Move follows engineering chief talking a leave of absence and the departure of another senior executive

Tesla Inc. TSLA -1.96% will restructure and flatten its management, Chief Executive Elon Musk told employees Monday, as the Silicon Valley automaker struggles to boost production of its Model 3 sedan amid an exodus of top leaders

Mr. Musk made the announcement following news that his engineering chief, Doug Field, was taking a leave of absence, and that senior executive Matthew Schwall was leaving the company for Alphabet Inc.’s GOOGL +0.64% driverless car division Waymo.

“To ensure that Tesla is well prepared for the future, we have been undertaking a thorough reorganization of our company,” Mr. Musk said in the memo reviewed by The Wall Street Journal. “As part of the reorg, we are flattening the management structure to improve communication, combining functions where sensible and trimming activities that are not vital to the success of our mission.”

He added that the company will continue to hire workers. In early May, Mr. Musk alluded to a reorganization when he discussed cutting down on the number of contract workers.

Under a flat management structure, employees work for top leaders with few layers of managers in between. But at Tesla, Mr. Musk is already in the trenches, sleeping on the factory floor as he tries to increase production of the Model 3, which began assembly last July and is months behind in reaching milestones.

Mr. Musk already has taken command of several significant roles. In February, the CEO announced the company’s sales and service divisions would report directly to him following the departure of Jon McNeill, Tesla’s president of global sales, marketing and delivery and service. He left to become chief operating officer at ride-hailing service Lyft Inc.

In April, Mr. Musk said he would take control of vehicle production from Mr. Fields, who was given those duties a year earlier on top of his engineering oversight.

Mr. Musk didn’t mention any names in the memo Monday or provide more details about any changing positions.

The management moves come at a critical juncture for Tesla as it tries to produce enough of its mass-market Model 3 sedans to generate cash to fund the business and instill confidence in investors that the company can move beyond being a niche-product maker.

The company is under pressure to meet a twice-delayed goal of building 5,000 Model 3s a week by around the end of June. Analysts say Tesla can start generating cash once it meets that milestone. Mr. Musk has said he expects the company to be profitable in the third quarter.

Excitement about Tesla’s ability to bring electric vehicles to the masses and then to develop autonomous vehicle technology helped push the company’s stock to record levels last year and give it a market value that rivals that of General Motors Co.

Tesla’s stock is down more than 5% so far this year. The shares were recently trading up about 0.6% at $302.83 in morning trading.

Mr. Field, a leader at the auto maker since joining in 2013 from Apple Inc., oversees the engineering of Tesla’s vehicles.

Mr. Schwall was the company’s main technical contact with U.S. safety investigators as the Silicon Valley auto maker races to develop driverless-car technology. His departure comes as the National Transportation Safety Board has been investigating multiple crashes.